Continuum-Level Analytical Model for Solid Oxide Fuel Cells with Mixed Conducting Electrolytes

A continuum-level analytical model was developed for the performance of solid oxide fuel cells (SOFCs) with mixed conducting electrolytes. The model was derived by coupling the Nernst-Planck equation for mass transport in the bulk with the Butler-Volmer equation for mass transport across an interface and by employing defect thermodynamics for boundary values. This approach allowed the usual assumptions of reversible electrodes and linear potential gradients (across the electrolyte) to be removed, thereby resulting in boundary defect concentrations that depend on potential (SOFC operating conditions) and allowing non-ohmic responses in mixed conducting electrolytes. Using only three fitting parameters, the authors validated the model through successful fits to experimental data from SOFCs with samaria- and gadolinia-doped ceria electrolytes, which are presently the mixed conducting electrolytes of greatest interest. The fits also allowed valuable information to be extracted from the experimental data regarding the overpotentials in the SOFC. Significantly, the anode, cathode, and electrolyte overpotentials were uniquely determined, each as a function of current. Hence, it was confirmed that performance losses due to electronic leakage through ceria electrolytes is confined to low load (low current and high voltage) conditions. Finally, the model was used to show that open-circuit voltage is a function of electrolyte thickness.